Alright, let's solve this problem step by step. We have 4076 and 9569 and we're adding them together.

Step 1: We'll start by adding the digits 6 & 9 in column 1 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 6 in column 2 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 0 & 5 in column 3 and get 6.

Step 4: We'll start by adding the digits 4 & 9 in column 4 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

So, 4076 + 9569 = 13645.

